For volume image reconstruction, an iterative algorithm has been developed by various groups. One exemplary algorithm is a total variation (TV) minimization iterative reconstruction algorithm for various applications including sparse views and limited angle x-ray CT reconstruction. Another exemplary algorithm is. a TV minimization algorithm aimed at region-of-interest (ROI) reconstruction with truncated projection data in many views, i.e., interior reconstruction problem. Yet another exemplary algorithm is a prior image constrained compressed sensing (PICCS) method. Total-variation-based iterative reconstruction (IRTV) algorithms have advantages for sparse view reconstruction problems.
In the prior art attempts, the data processing procedure of well-known IRTV algorithms is illustrated in FIG. 1. For example, simultaneous algebraic reconstruction technique (SART) generates the computed projection data from the image volume and back-projects the normalized difference between the measured projection and the computed projection data to reconstruct an updated image volume. In general, the sharpness is resulted due to a reduced number of errors in matching the real data while noise is increased in the updated image. As a result, the update image may appear sharp but noisy at the same time. Then, the updated image volume is regularized by total variation (TV) minimization routine in order to reduce noise at the cost of resolution.
The first prior art processing procedure as illustrated in FIG. 1 is of a sequential scheme. That is, the TV module follows the SART or alternatively projection on convex sets (POCS) module. The original image x(n−1) is processed by the SART routine to reduce an error amount in matching the real data and outputs an intermediate image or image update xSART(n), which now has an increased amount of noise. As the intermediate image or image update xSART(n) is obtained at an improved level of resolution, the original image x(n−1) is updated based upon the image update xSART(n). Then, the intermediate image xSART(n)is processed by the TV routine to reduce noise and generate an output image x(n), which now has an increased amount of the error. As the output image update x(n) is obtained, the original image x(n−1) is updated based upon the output image x(n) . Due to the above described sequential nature of the processing, the effect of the SART routine initially reduces the error while the TV routine improves the noise in a disjointed manner with regaining the error. Consequently, it still remains desirable to control the noise-resolution trade-off.
The second prior art processing procedure as illustrated in FIG. 2 has the same sequential scheme of performing SART first and then TV except for the generation of the output image x(n). Despite the difference, the procedure in FIG. 2 generally yields the same undesirable characteristics as described with respect to the procedure in FIG. 1. The original image x(n−1) is processed by the SART routine to reduce an error amount in matching the real data and outputs a first intermediate image or image update xSART(n), which now has an increased amount of noise. As the first intermediate image xSART(n) is obtained at an improved level of resolution, the original image x(n−1) is updated based upon the first intermediate image xSART(n). Then, the first intermediate image xSART(n) is processed by the TV routine to reduce noise and generate a second intermediate image xREG(n), which now has an increased amount of the error. As the second intermediate image xREG(n) is obtained, the second intermediate image xREG(n) and the first intermediate image xSART(n) are summed together to obtain an output image x(n), the original image x(n−1) is updated based upon the output image x(n). Although the procedure in FIG. 2 has a parameter λ for manually controlling the effects of SART first and then TV, it still remains desirable to control the noise-resolution trade-off.